Using the simulation parameters given in [1]}, we may generate the unknown counterfactual outcomes \(\theta \)  and simulate \(X\)  to measure the coverage rates of our confidence intervals. In 10K simulations, the 95% confidence intervals for \(\tau \)  had the desired 95% coverage probability, while the 95% interval for \(\xi _1\)  was 1.2 times wider than necessary and had coverage of 98%, and the 95% interval for \(\phi _1\)  was 1.75 times wider than necessary and had coverage of 99.9%. However, values for \(\theta \)  could be found such that the coverage of the interval for \(\phi _1\)  was as low as 96%, suggesting that the width of the confidence interval was necessary in order to have coverage of the estimand for all possible values of \(\theta \) , as required without further assumptions.
